Question: Express this quotient in scientific notation: ${\frac{1.080\times 10^{-2}} {3.0\times 10^{-3}}}$
Answer: Start by collecting like terms together. $= {\frac{1.080} {3.0}} \times{\frac{10^{-2}} {10^{-3}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.36 \times 10^{-2\,-\,-3}$ $= 0.36 \times 10^{1}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.36$ is the same as $3.60 \div 10$ , or $3.60 \times 10^{-1}$ $ = {3.60 \times 10^{-1}} \times 10^{1} $ $= 3.60\times 10^{0}$